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DOE OSTI2021

r 2 SCAN-D4: Dispersion corrected meta-generalized gradient approximation for general chemical applications

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r 2 SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, and non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal–organic systems transfers to condensed systems, where lattice energies of molecular crystals are within the chemical accuracy (errors <1 kcal/mol).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Self-interaction correction in water–ion clusters

We study the importance of self-interaction errors in density functional approximations for various water–ion clusters. We have employed the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method in conjunction with LSDA, PBE, and SCAN to describe binding energies of hydrogen-bonded water–ion clusters, i.e., water–hydronium, water– hydroxide, water–halide, as well as non-hydrogen-bonded water–alkali clusters. In the hydrogen-bonded water–ion clusters, the building blocks are linked by hydrogen atoms, although the links are much stronger and longer-ranged than the normal hydrogen bonds between water molecules, because the monopole on the ion interacts with both permanent and induced dipoles on the water molecules. We find that self-interaction errors overbind the hydrogen-bonded water– ion clusters and that FLOSIC reduces the error and brings the binding energies into closer agreement with higher–level calculations. Here, the non-hydrogen-bonded water–alkali clusters are not significantly affected by self-interaction errors. Self-interaction corrected PBE predicts the lowest mean unsigned error in binding energies (≤ 50 meV/H 2 O) for hydrogen-bonded water–ion clusters. Self-interaction errors are also largely dependent on the cluster size, and FLOSIC does not accurately capture the subtle variation in all clusters, indicating the need for further refinement.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Vertical detachment energies of ammonia cluster anions using self-interaction-corrected methods

Systems with weakly bound extra electrons impose great challenges to semilocal density functional approximations (DFAs), which suffer from self-interaction errors. Small ammonia clusters are one such example of weakly bound anions where the extra electron is weakly bound. We applied two self-interaction correction (SIC) schemes, viz., the well-known Perdew–Zunger and the recently developed locally scaled SIC (LSIC) with the local spin density approximation (LSDA), Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA), and the SCAN meta-GGA functionals to calculate the vertical detachment energies (VDEs) of small ammonia cluster anions (NH3)n–. Our results show that the LSIC significantly reduces the errors in calculations of VDE with LSDA and PBE-GGA functionals leading to better agreement with the reference values calculated with coupled cluster singles and doubles with perturbative triples [CCSD(T)]. Accurate prediction of VDE as an absolute of the highest occupied molecular orbital (HOMO) is challenging for DFAs. Our results show that VDEs estimated from the negative of HOMO eigenvalues with the LSIC-LSDA and Perdew–Zunger SIC-PBE are within 11 meV of the reference CCSD(T) results. Here, the LSIC method performs consistently well for the VDE estimates, from both the total energy differences and the absolute HOMO eigenvalues.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Comparing GGA, GGA+ U , and meta-GGA functionals for redox-dependent binding at open metal sites in metal–organic frameworks

Metal–organic frameworks (MOFs) with open metal sites have been widely investigated for the selective adsorption of small molecules via redox mechanisms where charge transfer can take place between the binding site and the adsorbate of interest. Quantum-chemical screening methods based on density functional theory have emerged as a promising route to accelerate the discovery of MOFs with enhanced binding affinities toward various adsorbates. However, the success of this approach is linked to the accuracy of the underlying density functional approximations (DFAs). In this work, we compare commonly used generalized gradient approximation (GGA), GGA+U, and meta-GGA exchange-correlation functionals in modeling redox-dependent binding at open metal sites in MOFs using O 2 and N 2 as representative small molecules. We find that the self-interaction error inherent to the widely used Perdew, Burke, and Ernzerhof (PBE) GGA predicts metal sites that are artificially redox-active, as evidenced by their strong binding affinities, short metal–adsorbate bond distances, and large degree of charge transfer. The incorporation of metal-specific, empirical Hubbard U corrections based on the transition metal oxide literature systematically reduces the redox activity of the open metal sites, often improving agreement with experiment. Additionally, the binding behavior shifts from strong chemisorption to weaker physisorption as a function of U. The M06-L meta-GGA typically predicts binding energies between those of PBE-D3(BJ) and PBE-D3(BJ)+U when using empirically derived U values from the transition metal oxide literature. Despite the strong sensitivity of the binding affinities toward a given DFA, the GGA, GGA+U, and meta-GGA approaches often yield the same qualitative trends and structure–property relationships.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Delocalization error poisons the density-functional many-body expansion

The many-body expansion is a fragment-based approach to large-scale quantum chemistry that partitions a single monolithic calculation into manageable subsystems. This technique is increasingly being used as a basis for fitting classical force fields to electronic structure data, especially for water and aqueous ions, and for machine learning. Here, we show that the many-body expansion based on semilocal density functional theory affords wild oscillations and runaway error accumulation for ion–water interactions, typified by F − (H 2 O) N with N ≳ 15. We attribute these oscillations to self-interaction error in the density-functional approximation. The effect is minor or negligible in small water clusters, explaining why it has not been noticed previously, but grows to catastrophic proportion in clusters that are only moderately larger. This behavior can be counteracted with hybrid functionals but only if the fraction of exact exchange is ≳50%, whereas modern meta-generalized gradient approximations including ωB97X-V, SCAN, and SCAN0 are insufficient to eliminate divergent behavior. Other mitigation strategies including counterpoise correction, density correction (i.e., exchange–correlation functionals evaluated atop Hartree–Fock densities), and dielectric continuum boundary conditions do little to curtail the problematic oscillations. In contrast, energy-based screening to cull unimportant subsystems can successfully forestall divergent behavior. These results suggest that extreme caution is warranted when the many-body expansion is combined with density functional theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Status and Challenges of Density Functional Theory

Here, we discuss some of the challenges facing density functional theory (DFT) and recent progress in DFT for both ground and excited electronic states. We discuss key aspects of the results we have been able to obtain with the strategy of designing density functionals to have various ingredients and functional forms that are then optimized to accurately predict various types of properties and systems with as much universality as possible. Finally, we make specific recommendations of approximate density functionals that are well suited for particular kinds of applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Machine learning for impurity charge-state transition levels in semiconductors from elemental properties using multi-fidelity datasets

Quantifying charge-state transition energy levels of impurities in semiconductors is critical to understanding and engineering their optoelectronic properties for applications ranging from solar photovoltaics to infrared lasers. While these transition levels can be measured and calculated accurately, such efforts are time-consuming and more rapid prediction methods would be beneficial. Here, we significantly reduce the time typically required to predict impurity transition levels using multi-fidelity datasets and a machine learning approach employing features based on elemental properties and impurity positions. We use transition levels obtained from low-fidelity (i.e., local-density approximation or generalized gradient approximation) density functional theory (DFT) calculations, corrected using a recently proposed modified band alignment scheme, which well-approximates transition levels from high-fidelity DFT (i.e., hybrid HSE06). Further, the model fit to the large multi-fidelity database shows improved accuracy compared to the models trained on the more limited high-fidelity values. Crucially, in our approach, when using the multi-fidelity data, high-fidelity values are not required for model training, significantly reducing the computational cost required for training the model. Our machine learning model of transition levels has a root mean squared (mean absolute) error of 0.36 (0.27) eV vs high-fidelity hybrid functional values when averaged over 14 semiconductor systems from the II–VI and III–V families. As a guide for use on other systems, we assessed the model on simulated data to show the expected accuracy level as a function of bandgap for new materials of interest. Finally, we use the model to predict a complete space of impurity charge-state transition levels in all zinc blende III–V and II–VI systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

How well do self-interaction corrections repair the overestimation of static polarizabilities in density functional calculations?

Herein, we examine the effect of removing self-interaction error (SIE) on the calculation of molecular polarizabilities in the local spin density (LSDA) and generalized gradient approximations (GGA). To this end, we utilize a database of 132 molecules taken from a recent benchmark study [Hait and Head-Gordon, Phys. Chem. Chem. Phys. , 2018, 20 , 19800] to assess the influence of SIE on polarizabilities by comparing results with accurate reference data. Our results confirm that the general overestimation of molecular polarizabilities by these density functional approximations can be attributed to SIE. However, removing SIE using the Perdew–Zunger self-interaction-correction (PZ-SIC) method, implemented using the Fermi–Löwdin Orbital SIC approach, leads to an underestimation of molecular polarizabilities, showing that PZ-SIC overcorrects when combined with LSDA or GGA. Application of a recently proposed locally scaled SIC [Zope, et al., J. Chem. Phys. , 2019, 151 , 214108] is found to provide more accurate polarizabilities. We attribute this to the ability of the local scaling scheme to selectively correct for SIE in the regions of space where the correction is needed most.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Construction of meta-GGA functionals through restoration of exact constraint adherence to regularized SCAN functionals

The strongly constrained and appropriately normed (SCAN) meta-GGA exchange–correlation functional is constructed as a chemical environment-determined interpolation between two separate energy densities: one describes single-orbital electron densities accurately and another describes slowly varying densities accurately. To conserve constraints known for the exact exchange–correlation functional, the derivatives of this interpolation vanish in the slowly varying limit. While theoretically convenient, this choice introduces numerical challenges that degrade the functional’s efficiency. We have recently reported a modification to the SCAN meta-GGA, termed restored-regularized-SCAN (r 2 SCAN) , that introduces two regularizations into SCAN, which improve its numerical performance at the expense of not recovering the fourth order term of the slowly varying density gradient expansion for exchange. Here, we show the derivation of a progression of density functional approximations [regularized SCAN (rSCAN), r++SCAN, r 2 SCAN, and r 4 SCAN] with increasing adherence to exact conditions while maintaining a smooth interpolation. The greater smoothness of r 2 SCAN seems to lead to better general accuracy than the additional exact constraint of SCAN or r 4 SCAN does.

, correlation energy↗
DOE OSTI2020

Molecule-surface interaction from van der Waals-corrected semilocal density functionals: The example of thiophene on transition-metal surfaces

Semilocal density functional approximations are widely used. None of them can capture the long-range van der Waals (vdW) attraction between separated subsystems, but they differ remarkably in the extent to which they capture intermediate-range vdW effects responsible for equilibrium bonds between neighboring small closed-shell subsystems. The local density approximation (LDA) often overestimates this effect, while the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) underestimates it. The strongly constrained and appropriately normed (SCAN) meta-GGA often estimates it well. All of these semilocal functionals require an additive nonlocal correction such as the revised Vydrov-Van Voorhis 2010 (rVV10) to capture the long-range part. This work reports adsorption energies and the corresponding geometry of aromatic thiophene (C 4 H 4 S) bound to transition-metal surfaces. The adsorption process requires a genuine interplay of covalent and weak binding and requires a simultaneously accurate description of surface and adsorption energies with the correct prediction of the adsorption site. All these quantities must come from well-balanced short- and long-range correlation effects for a universally applicable method for weak interactions with chemical accuracy. Here, our methods indicate that the correct interplay is not present in any combination of recent meta-GGA's and rVV10. The simple short-range damping of the vdW correction scheme that is practically successful in the combination of GGA's and vdW approximations is less transferable in SCAN+rVV10 or in the revised version, revSCAN+rVV10. In addition, we present accurate random-phase-approximation-quality adsorption energies from a model based on the one of Zaremba and Kohn.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Predicting Mössbauer Parameters of Nonheme Diiron Complexes with Density Functional Theory

Mössbauer spectroscopy provides significant insights into the electronic structure and environment of the metal centers. In this work, we investigate the electronic structures of a set of nonheme diiron complexes by evaluating two key parameters pertaining to Mössbauer spectroscopy, namely, the isomer shift (δ) and quadrupole splitting (|ΔE Q |), using different levels of density functional theory (DFT). The diiron systems investigated here span diverse oxidation states, bridging motifs, and spin coupling patterns, which present a challenging case for theoretical predictions. We demonstrate that the combination of B97-D3/def2-TZVP is an efficient approach in modeling both the δ and |ΔEQ| values with high accuracy for the representative nonheme diiron complexes. We also show that δ is accurately predicted irrespective of the choice of approximate density functional while the |ΔE Q | is sensitive to the level of theory employed. Further investigation shows that the present methodology assessed using synthetic nonheme diiron complexes could be extended to nonheme diiron enzyme active sites, featuring both ferromagnetic and antiferromagnetic coupling between the iron centers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Frontiers in Magnetic Materials

Magnetism is crucial to many modern technologies, a driver for condensed matter physics research and one of the most remarkable and diverse properties of matter. We propose to develop understanding of novel magnetism and magnetic related behavior in materials and use this to accelerate the discovery of forefront magnetic materials. The approach is via the connection of magnetic properties to specific structures and materials. Topics that will be addressed are (1) Metallic magnetic materials with unusually low carrier concentrations and/or moments (2) Magnetism arising from unusual chemistry including 4d and 5d magnetism and (3) Materials with strong spin-fluctuations, which can lead to quantum criticality, spin-fluctuation induced superconductivity and other novel quantum behavior. These topics overlap, for example, the 4d ruthenates include ferromagnets (perovskite SrRuO 3 ), extremely high ordering temperature antiferromagnets (honeycomb lattice SrRu 2 O 6 ) and well as quantum materials with strong spin fluctuations (layered perovskite Sr 2 RuO 4 and Sr 3 Ru 2 O 7 ). We will use of density calculations to connect magnetic properties with chemistry and structure and employ phenomenological theories to extend these results to properties that are not directly given by direct first principles methods and we will conduct tests to explore the limitations of density functional approximations and new functionals.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Self-interaction error overbinds water clusters but cancels in structural energy differences

Here, we gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi–Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew–Burke–Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction–corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/ H 2 O from about 42 meV/ H 2 O for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction–corrected SCAN. These findings suggest that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within “chemical accuracy” (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N7) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob’s ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N3 − N4) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.

Chemistry↗
DOE OSTI2023

The difference between molecules and materials: Reassessing the role of exact conditions in density functional theory

Exact conditions have long been used to guide the construction of density functional approximations. However, hundreds of empirical-based approximations tailored for chemistry are in use, of which many neglect these conditions in their design. We analyze well-known conditions and revive several obscure ones. Two crucial distinctions are drawn: that between necessary and sufficient conditions and that between all electronic densities and the subset of realistic Coulombic ground states. Simple search algorithms find that many empirical approximations satisfy many exact conditions for realistic densities and non-empirical approximations satisfy even more conditions than those enforced in their construction. The role of exact conditions in developing approximations is revisited.

Chemistry↗
DOE OSTI2023

Defect-induced states, defect-induced phase transition, and excitonic states in bent tungsten disulfide (WS 2 ) nanoribbons: Density functional vs. many body theory

Two-dimensional (2D) transition metal dichalcogenide (TMD) materials have versatile electronic and optical properties. TMD nanoribbons exhibit interesting properties due to reduced dimensionality, quantum confinement, and edge states, which make them suitable for various electronic and optoelectronic applications. In a previous work conducted by our group, we demonstrated that the edge bands evolved with bending can tune the optical properties for various widths of TMD nanoribbons. Defects are commonly present in 2D TMD materials, and can dramatically change the material properties. Here, in this following work, we investigate the interaction between the edge and the defect states in tungsten disulfide (WS 2 ) nanoribbons with lines of W- or S-atom vacancies defects under different bending conditions, using density functional theory (DFT). To gain understanding about the limits of density functional approximations, we compare results on band gaps and energies of defect states with quasiparticle GW. We reveal interesting semiconductor-metal phase transitions, suggesting potential applications in nanoelectronics or molecular electronics. We also calculate the optical absorption of the bent and defective nanoribbons with the many-body GW-BSE (Bethe-Salpeter equation) approach, revealing a tunable optical spectrum and diverse exciton states in the defective WS 2 nanoribbons.

36 MATERIALS SCIENCE↗
DOE OSTI2023

G 0 W 0 Ionization Potentials of First-Row Transition Metal Aqua Ions

Here, we report computations of the vertical ionization potentials within the GW approximation of the near-complete series of first-row transition metal (V–Cu) aqua ions in their most common oxidation states, i.e., V 3+ , Cr 3+ , Cr 2+ , Mn 2+ , Fe 3+ , Fe 2+ , Co 2+ , Ni 2+ , and Cu 2+ . The d-orbital occupancy of these systems spans a broad range from d 2 to d 9 . All of the structures were first optimized at the density functional theory level using a large cluster of explicit water molecules that are embedded in a continuum solvation model. Vertical ionization potentials were computed with the one-shot G 0 W 0 approach on a range of transition metal ion clusters (6, 18, 40, and 60 explicit water molecules), wherein the convergence with respect to the basis set size was evaluated using the systems with 40 water molecules. We assess the results using three different density functional approximations as starting points for the vertical ionization potential calculations, namely, G 0 W 0 @PBE, G 0 W 0 @PBE0, and G 0 W 0 @r 2 SCAN. While the predicted ground-state structures are similar to all three exchange-correlation functionals, the vertical ionization potentials were in closer agreement with experiment when using the G 0 W 0 @PBE0 and G 0 W 0 @r 2 SCAN approaches, with the r 2 SCAN-based calculations being significantly less expensive. Computed bond distances and vertical ionization potentials for all structures are in good agreement with available experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Exact constraints and appropriate norms in machine-learned exchange-correlation functionals

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human-designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently, efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to de-orbitalize the strongly constrained and appropriately normed (SCAN) functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding the use of the orbital-dependent kinetic energy density. The performance and transferability of the machine-learned functional are demonstrated for molecular and periodic systems.

Artificial neural networks↗